Problem 8. Find all primes p such that both p − 2 and p + 2 are prime. (Make sure to show that you proved that you found all such p.) Hint: Consider three cases p = 3k, p = 3k + 1, and p = 3k + 2. Problem 8. Find all primes p such that both p - 2 and p+2 are prime. (Make sure to showthat you proved that you found all such p.) Hint: Consider three cases p= 3k, p= 3k + 1, andp=3k + 2.

Any prime number (in general any number) p can be written in either of the following form: p =…

Answered: Problem 8. Find all primes p such that…

Problem 8. Find all primes p such that both p − 2 and p + 2 are prime. (Make sure to show that you proved that you found all such p.) Hint: Consider three cases p = 3k, p = 3k + 1, and p = 3k + 2.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.1: Real Numbers

Problem 34E

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Question

Problem 8. Find all primes p such that both p − 2 and p + 2 are prime. (Make sure to show that you proved that you found all such p.) Hint: Consider three cases p = 3k, p = 3k + 1, and p = 3k + 2.